Will Kybella work for stubborn above the elbow fat? (photo)

Kybella is indicated for the chin area. It would decrease the fat, but it is not the best procedure for you. 
Smartlipo is a better option. It will remove the fat and tighten the skin of your arms.

Kybella is only approved to treat submental fat under the chin. I do not believe it would be effective in this area. It could require so many treatments that it would be much more expensive than liposuction and it could injure a nerve in this area. Instead, I would recommend liposuction to remove the isolated areas of fat above the elbow. Liposuction gently suctions away the fat cells via micro-cannulas. The small cannula pushes aside nerves and vessels and is very safe. The procedure can be performed using local anesthetic and recovery is typically just a few days.
If skin laxity is also a concern, you can combine liposuction with a nonsurgical skin tightening treatment known as ThermiTight. This procedure delivers radiofrequency deep into the dermal layers, constricting tissue and increasing collagen levels. I advise you to find a board-certified dermatologist with extensive experience in this type of body contouring to ensure your treatment is both safe and successful. 

this likely needs liposuction by alternative treatments like kybella and/or truscupt ID can help.this are needs a lot of caution! often women are very loose here and if you overdo liposuction you will be smaller and more contoured but have loose skin and creepiness.  this often needs a thigh or knee lift IF very loose.  If a candidate, then liposuction + internal heating with renuvion/j plasma or Inmode BodyTite maybe able to help.  Alternative non invasive treatments are Coolsculpting, TrusculptID, kybella, PDO or Instalift threads.  Morpheus deep Microneedling RF and RF treatments like Venus legacy, forma/contoura, or exilis should be done regularly to maintain. the results.  Best, Dr. Emer.

Kybella is one of the most effective non surgical treatments to dissolve / remove stubborn fat deposits, it requires sessions. There are some areas off the label who can be treated besides the neck. In the right hands its a very effective treatment to remove fat deposits. Make sure you go with and expert and set a plan to achieve the best results. Good luck. 
Dr Luis Salazar
Aesthetic Solutions

Trusculpt ID causes fat destruction and skin tightening.   Trusculpt ID is not dependent on suction for effect and was not restricted in BMI in trials.   Using a device that causes tightening and fat destruction will offer more global benefit.

Maybe but the # of sessions would be at least 3-6 with all time in between them. Plus the cost of 3 sessions would be >$4,000....with unpredictable results. I might try localized liposuction with small diameter cannulae, than heal for few months followed with Kybella  1 session. Fee $5,000 range.